Computer Security Resource Center

Computer SecurityResource Center

Pairing-Based Cryptography

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Recently, what are known as “pairings” on elliptic curves have been a very active area of research in cryptography. A pairing is a function that maps a pair of points on an elliptic curve into a finite field. Their unique properties have enabled many new cryptographic protocols that had not previously been feasible.

In particular, identity-based encryption (IBE) is a pairing-based scheme that has received considerable attention. IBE uses some form of a person (or entity’s) identification to generate a public key. This could be an email address, for instance. An IBE scheme allows a sender to encrypt a message without needing a receiver’s public key to have been certified and distributed for subsequent use. Such a scenario is quite useful if the pre-distribution of public keys is impractical. Besides IBE, there are a number of other applications of pairing-based cryptography. These include many other identity-based cryptosystems (including signature schemes), key establishment schemes, functional and attribute-based encryption, and privacy-enhancing techniques, such as the use of anonymous credentials.

In 2008, NIST held a workshop on pairing-based cryptography. While the workshop showed that there was interest in pairing-based schemes, a common understanding was that further study was needed before NIST approved any such schemes. Starting in 2011, members of the Cryptographic Technology Group have conducted an extensive study on pairing-based cryptographic schemes. This included topics such as: the construction of pairing-friendly elliptic curves, a survey of pairing-based cryptographic schemes, implementation efficiency with respect to the required security, standard activities involving pairing-based schemes, use cases and practical implications. This study was summarized in a technical report, Report on Pairing-based Cryptography, written in 2012, and published in the NIST Journal of Research in 2015.

Pairing operations appear to be important tools for various cryptographic schemes used in cloud computing and privacy enhancing environments. Besides IBE, other demanding applications have also motivated the continuation of this study. Short signatures and broadcast encryption are examples of such applications.